Free AIME Combinatorics Questions and Answers

Question 1

How many ways can 5 people be seated in a row?

Accepted Answer

120

Answer

24

Answer

60

Answer

720

Question 2

In how many ways can a committee of 3 people be chosen from a group of 10?

Accepted Answer

120

Answer

30

Answer

45

Answer

720

Question 3

How many ways can the letters of the word "AIME" be arranged?

Accepted Answer

24

Answer

12

Answer

120

Answer

720

Question 4

How many ways can you distribute 5 identical candies to 3 children so that each child gets at least one candy?

Accepted Answer

10

Answer

6

Answer

21

Answer

15

Question 5

In how many ways can you choose 2 different cards from a standard deck of 52 cards?

Accepted Answer

1326

Answer

1378

Answer

1324

Answer

1348